Almost quantum correlations violate the no-restriction hypothesis

TL;DR

This paper demonstrates that almost quantum correlations cannot be reproduced by theories satisfying the no-restriction hypothesis, highlighting the hypothesis's potential role in distinguishing quantum correlations from other non-signalling correlations.

Contribution

It proves that theories obeying the no-restriction hypothesis cannot generate almost quantum correlations, emphasizing the hypothesis's significance in quantum correlation characterization.

Findings

Almost quantum correlations cannot be reproduced under the no-restriction hypothesis.

The no-restriction hypothesis may be fundamental in identifying quantum correlations.

The results suggest the necessity of measurement restrictions to reproduce almost quantum correlations.

Abstract

To identify which principles characterize quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost quantum correlations. We solve this problem by invoking the so-called no-restriction hypothesis, an explicit and natural axiom in many reconstructions of quantum theory stating that the set of possible measurements is the dual of the set of states. We prove that, contrary to quantum correlations, no generalised probabilistic theory satisfying the no-restriction hypothesis is able to reproduce the set of almost quantum correlations. Therefore, any theory whose correlations are exactly, or very close to, the almost quantum correlations necessarily requires a rule limiting the possible measurements. Our results suggest that the no-restriction hypothesis may play a fundamental role in singling out the set of quantum correlations among other non-signalling ones.